Constraints - 
As mentioned earlier in the introduction, the theoretical description of
fission involves mapping out the variations of the total energy as a function
of the deformation of the fissioning nucleus. In phenomenological models based
on the macroscopic-microscopic method, this is achieved by parameterizing the
nuclear shape; in the HFB theory, this requires seeking solutions of the HFB
equation (REF ) with constraints on the expectation value of
operators associated with the nuclear shape. The simplest example of such
operators are the multipole moments (computed in the intrinsic frame of
reference): \(\hat{Q}_{\lambda \mu } = c_{\lambda \mu }r^{\lambda }Y_{\lambda \mu }\) ,
where \(c_{\lambda \mu }\)  is a normalization constant and \(Y_{\lambda \mu }\)  are the
spherical harmonics [1]}. Let us note
\(\lbrace  \hat{F}_{a} \rbrace _{a=1,\dots ,N}\)  the set of \(N\)  operators on which expectation
value we seek to impose a constraint. This can be achieved by the standard
method of Lagrange parameters: instead of minimizing the total energy
\(E[\rho ,\kappa ,\kappa ^*]\) , we minimize instead
\(\mathcal {E} = E - \sum _{a} (\mathinner {\langle {\hat{F}_a}\rangle } - \bar{F}_a)\) , where
\(\bar{F}_a\)  is the target value for the constraint and \(\mathinner {\langle {\hat{F}_a}\rangle } =\mathrm {Tr}(\hat{F}_a\rho )\)  the expectation value (here assuming a one-body
operator only). It is straightforward to see that the HFB matrix is modified
and becomes
\(\mathcal {H} = \left( \begin{array}{cc}h - \sum _a F_{a} & \Delta \\-\Delta ^{*} & -h^{*} + \sum _a F^{*}_{a}\end{array}\right),\) 
